Question

graph the line.
$y = \frac{1}{2}x - 3$

Explanation:

Step1: Identify the slope and y - intercept

The equation of the line is in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=\frac{1}{2}x - 3\), the slope \(m=\frac{1}{2}\) and the y - intercept \(b=- 3\).

Step2: Plot the y - intercept

The y - intercept is \(b = - 3\), so we plot the point \((0,-3)\) on the y - axis.

Step3: Use the slope to find another point

The slope \(m=\frac{1}{2}=\frac{\text{rise}}{\text{run}}\). From the point \((0,-3)\), we move up 1 unit (rise) and then move 2 units to the right (run) because the slope is positive. This gives us the point \((0 + 2,-3+1)=(2,-2)\). We can also move down 1 unit and left 2 units from \((0,-3)\) to get another point \((0 - 2,-3 - 1)=(-2,-4)\).

Step4: Draw the line

Draw a straight line through the points \((0,-3)\), \((2,-2)\) (or other points found using the slope) to graph the line \(y=\frac{1}{2}x-3\).

(Note: Since this is a graphing problem, the final answer is the graph of the line \(y = \frac{1}{2}x-3\) passing through points like \((0,-3)\), \((2,-2)\), \((-2,-4)\) etc. If we were to describe the key points: the y - intercept is at \((0,-3)\) and using the slope \(\frac{1}{2}\), we can find additional points to draw the line.)

Answer:

The line \(y=\frac{1}{2}x - 3\) is graphed by plotting the y - intercept \((0,-3)\) and then using the slope \(\frac{1}{2}\) to find other points (e.g., \((2,-2)\), \((-2,-4)\)) and drawing a straight line through them.